The latter part of the paper is dedicated to showing that the OPE coefficients derived from Poincaré symmetry respect the algebra generated by the infinite tower of conformally soft graviton currents in minimally-coupledCorrections to the generalized soft theorems from higher-derivative effective field operators are absent in minimally-coupled theories of gravity [1]}, [2]}. It would be very interesting and nontrivial to understand the deformation of the symmetry algebra and ensuing OPE constraints that are induced by these corrections. We leave this open problem to a future investigation. tree-level gravitational theories. To do so, we explicitly construct currents and show that they generate the action of \({\rm w}_{1 +\infty }\)  on massless celestial operators. The construction of the currents involves a light transform [3]}, which has played an increasingly important role in celestial holography [4]}, [5]}, [6]}, [7]}. As before, our approach is manifestly 2D conformally covariant. In this approach, the \({\rm SL}(2, \mathbb {R})\)  subalgebra of \({\rm w}_{1 +\infty }\)  is readily identified as the right-moving \({\rm SL}(2, \mathbb {R})\)  global conformal symmetry upon analytic continuation to the celestial torus [8]}. Another auxiliary result in this work is a simple and explicit construction of the scalar primary operator that generates supertranslations and was previously discussed in [9]}, [10]}, [11]}, [12]}.
